I'm in a C tuning on a J200 at the moment - it is absolutely fine on medium gauge strings and the big old body of teh beast really makes the notes sing, my partner though is using the D'Addario heavies on a smaller bodied guitar(green pack I think)and that reduced any slight rattle from the string slackness and gave a richer bass tone. also on the mediums i found the top string was sounding a wee bit thin and sharper in sound than before but then I have not long put brass pegs on them so that might be a contributing factor and I am just not used to them!
I have to say though that the poor old box felt like it was screaming when it went back into standard after being in C for so long - I would say if you are thinking of regularly playing in C tunings if you can do have a guitar tuned just in C to save on stressing the neck.....and as a good excuse to get another guitar
:-D